Day 1

1
Day 1
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Momentum and Its Conservation

2
After Attendance(EQ Sheet Concept Map)
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Place HW on my desk
• Pickup a new Essential Question Sheet
• Pickup and sign out your computer
• Log into www.plutonium-239.com
• Select the Warm-Up link
• Complete todays warm-up and submit it
• Logout and return the computer to the cart
• Pull out your Conservation of Energy and
  Momentum Concept Map

3
Feed Back for Google Docs
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Was anything confusing on google docs?
• Noteworthy Student Responses

4
Review of Materials
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Conservation of Energy Test

5
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?
Chapter 7 Linear Momentum
6
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?
Units of Chapter 7

• Momentum and Its Relation to Force
• Conservation of Momentum
• Collisions and Impulse
• Conservation of Energy and Momentum in Collisions
• Elastic Collisions in One Dimension

7
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?
Units of Chapter 7

• Inelastic Collisions
• Collisions in Two or Three Dimensions
• Center of Mass (CM)
• CM for the Human Body
• Center of Mass and Translational Motion

8
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?
Equations to KnowLinear Momentum
9
Linear Momentum Conservation of Momentum

• EQ(s) How can the velocity of an object be
  quantified in terms of its momentum?

INSERT Picture Pushinga Car
Start What does it mean to gain momentum?
10
How can the velocity of an object be quantified
in terms of its momentum?
7-1 Momentum and Its Relation to Force
Momentum is a vector symbolized by the symbol p,
and is defined as The rate of change of
momentum is equal to the net force This can be
shown using Newtons second law.
(7-1)
(7-2)
11
How can the velocity of an object be quantified
in terms of its momentum?
7-2 Conservation of Momentum
During a collision, measurements show that the
total momentum does not change
(7-3)
12
How can the velocity of an object be quantified
in terms of its momentum?
7-2 Conservation of Momentum
More formally, the law of conservation of
momentum states The total momentum of an
isolated system of objects remains constant.
13
How can the velocity of an object be quantified
in terms of its momentum?
7-2 Conservation of Momentum
Momentum conservation works for a rocket as long
as we consider the rocket and its fuel to be one
system, and account for the mass loss of the
rocket.
14
Conservation of Momentum
How can the velocity of an object be quantified
in terms of its momentum?
What happens to an objects motion if it breaks
apart?
INSERT VIDEO CLIP
15
Conservation of Momentum
How can the velocity of an object be quantified
in terms of its momentum?
What happens to an objects motion if it breaks
apart?
INSERT VIDEO CLIP
16
Conservation of Momentum
How can the velocity of an object be quantified
in terms of its momentum?
What happens to an objects motion if it breaks
apart?
INSERT VIDEO CLIP
17
Conservation of Momentum
How can the velocity of an object be quantified
in terms of its momentum?
Another application of conservation of momentum
INSERT VIDEO CLIP
18
Conservation of Momentum
How can the velocity of an object be quantified
in terms of its momentum?
Another application of conservation of momentum
INSERT VIDEO CLIP
19
Conservation of Momentum
How can the velocity of an object be quantified
in terms of its momentum?
Another application of conservation of momentum
INSERT VIDEO CLIP
20
Pasco Momentum in Collisions LAB
How can the velocity of an object be quantified
in terms of its momentum?

• Work in groups of no more than 4 people.
• Return all supplies to the counter/cart.

INSERT LAB PICTURE
21
WebAssign/Lab Time
How can the velocity of an object be quantified
in terms of its momentum?

• Work on WebAssign Problems 7.1 - 7.6 or the Pasco
  Momentum in Collisions Lab
• Final Copy Criteria
• State the problem (Ex. Find displacement)
• Draw a picture/diagram
• Provide a list or table of all given data (Ex. ?t
  2 s)
• Solve the problem symbolically (Ex. v?x/?t ? ?x
  v?t)
• Plug in numbers and units to obtain answer. (Ex.
  ?x (5 m/s)(2 s) 10 m)
• Notes about WebAssign
• Positive vs. negative answers (Try a negative
  sign)
• Look at the final unit (hours or minutes or
  seconds)

22
How can the velocity of an object be quantified
in terms of its momentum?
Summary

• Answer the Essential Questions.
• Ticket out the Door
• What is the formula for momentum?
• What is the formula that relates force and
  momentum?
• If two objects have the same momentum, are they
  going at the same speed? Explain.
• HW
• Pasco Momentum in Collisions Lab (Questions and
  Conclusions)
• WebAssign Problems 7.1 - 7.6
• MIDTERM

INSERTPICTURE TBD
23
Day 2
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Collisions and Impulse

24
After Attendance
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Place HW on my desk
• Pickup and sign out your computer
• Log into www.plutonium-239.com
• Select the Warm-Up link
• Complete todays warm-up and submit it
• Logout and return the computer to the cart

25
Feed Back for Google Docs
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Was anything confusing on google docs?
• Noteworthy Student Responses

26
Review of Materials
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Yesterdays TOTD WebAssign Questions

27
Linear Momentum Collisions and Impulse

• EQ(s) How are momentum, impulse, and force
  related?

INSERT Picture Falling Kid
Start Why do some of us naturally put our hands
out to break our fall?
28
How are momentum, impulse, and force related?
7-3 Collisions and Impulse
During a collision, objects are deformed due to
the large forces involved. Since , we can
write The definition of impulse
(7-5)
29
Pasco Momentum in Collisions and Impulse
How are momentum, impulse, and force related?
How much deformation takes place during a
collision?
INSERT VIDEO CLIPTime Warp - Mangini Cymbal
Hit
30
Pasco Momentum in Collisions and Impulse
How are momentum, impulse, and force related?
How much deformation takes place during a
collision?
INSERT VIDEO CLIPTime Warp - Mangini Cymbal
Hit
31
Pasco Momentum in Collisions and Impulse
How are momentum, impulse, and force related?
How much deformation takes place during a
collision?
INSERT VIDEO CLIPTime Warp - Mangini Cymbal
Hit
32
How are momentum, impulse, and force related?
7-3 Collisions and Impulse
Since the time of the collision is very short, we
need not worry about the exact time dependence of
the force, and can use the average force. This
spike is known as the delta function.
33
Pasco Momentum in Collisions and Impulse
How are momentum, impulse, and force related?
How could we calculate the collision time?
INSERT VIDEO CLIPTime Warp - Mangini 1206
34
Pasco Momentum in Collisions and Impulse
How are momentum, impulse, and force related?
How could we calculate the collision time?
INSERT VIDEO CLIPTime Warp - Mangini 1206
35
Pasco Momentum in Collisions and Impulse
How are momentum, impulse, and force related?
How could we calculate the collision time?
INSERT VIDEO CLIPTime Warp - Mangini 1206
36
How are momentum, impulse, and force related?
7-3 Collisions and Impulse
The impulse tells us that we can get the same
change in momentum with a large force acting for
a short time, or a small force acting for a
longer time.
This is why you should bend your knees when you
land why airbags work and why landing on a
pillow hurts less than landing on concrete.
37
How are momentum, impulse, and force related?
Collisions and Impulse Demonstrations
Happy and Sad Ball Meet the Board of Education
Can they knock over the block? Egg Throw Can you
break the egg?
38
Pasco Momentum in Collisions LAB
How are momentum, impulse, and force related?

• Work in groups of no more than 4 people.
• Return all supplies to the counter/cart.

INSERT LAB PICTURE
39
WebAssign/Lab Time
How are momentum, impulse, and force related?

• Work on WebAssign Problems 7.1 - 7.11, or the
  Pasco Momentum in Collisions Lab
• Final Copy Criteria
• State the problem (Ex. Find displacement)
• Draw a picture/diagram
• Provide a list or table of all given data (Ex. ?t
  2 s)
• Solve the problem symbolically (Ex. v?x/?t ? ?x
  v?t)
• Plug in numbers and units to obtain answer. (Ex.
  ?x (5 m/s)(2 s) 10 m)
• Notes about WebAssign
• Positive vs. negative answers (Try a negative
  sign)
• Look at the final unit (hours or minutes or
  seconds)

40
How are momentum, impulse, and force related?
Summary

• Answer the Essential Questions.
• Ticket out the Door
• What is the formula for impulse?
• What happens to the change in momentum as the
  change in time increases?
• What happens to the force as the change in time
  increases?
• HW
• Pasco Momentum in Collisions Lab (Questions and
  Conclusions)
• WebAssign Problems 7.1 - 7.11

INSERTPICTURE Falling Kid
41
Day 3
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Elastic Collisions

42
After Attendance
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Place HW on my desk
• Pickup and sign out your computer
• Log into www.plutonium-239.com
• Select the Warm-Up link
• Complete todays warm-up and submit it
• Logout and return the computer to the cart

43
Feed Back for Google Docs
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Was anything confusing on google docs?
• Noteworthy Student Responses

44
Review of Materials
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Yesterdays TOTD WebAssign Questions

45
Linear Momentum Elastic Collisions

• EQ(s) How are momentum and kinetic energy
  related?How does the total momentum in an
  isolated system change?

INSERT Picture
Start What happens to the velocity of an object
after it collides with another object? Also, how
does a2 - b2 factor?
46
How are momentum and kinetic energy related? How
does the total momentum in an isolated system
change?
7-4 Conservation of Energy and Momentum in
Collisions
Momentum is conserved in all collisions. Collision
s in which kinetic energy is conserved as well
are called elastic collisions, and those in which
it is not are called inelastic.
47
How are momentum and kinetic energy related? How
does the total momentum in an isolated system
change?
7-5 Elastic Collisions in One Dimension
Here we have two objects colliding elastically.
We know the masses and the initial speeds. Since
both momentum and kinetic energy are conserved,
we can write two equations. This allows us to
solve for the two unknown final speeds.
48
How are momentum and kinetic energy related? How
does the total momentum in an isolated system
change?
7-5 Elastic Collisions in One Dimension
momentum
kinetic energy
Write down ? this equation
For a head-on elastic collision, the relative
speed of the two objects after the collision has
the same magnitude in the opposite direction as
before the collision, no matter what the masses
are.
49
How are momentum and kinetic energy related? How
does the total momentum in an isolated system
change?
7-5 Elastic Collisions in One Dimension
Solving for v'A
50
How are momentum and kinetic energy related? How
does the total momentum in an isolated system
change?
7-5 Elastic Collisions in One Dimension
Solving for v'B
Recall that
51
How are momentum and kinetic energy related? How
does the total momentum in an isolated system
change?
7-5 Elastic Collisions in One Dimension
Analyzing the solution for v'A and v'B
What happens if vB is equal to zero?
Write theseequationsdown
52
How are momentum and kinetic energy related? How
does the total momentum in an isolated system
change?
7-5 Elastic Collisions in One Dimension
Analyzing the solution for v'A and v'B
What happens if vB is equal to zero and mA is
much smaller than mB? (i.e. mA mB mA 0
compared to mB)
Does ?
Is this what we expect?
Is it amazing?
no.
53
How are momentum and kinetic energy related? How
does the total momentum in an isolated system
change?
7-5 Elastic Collisions in One Dimension
Analyzing the solution for v'A and v'B
What happens if vB is equal to zero and mA is
much larger than mB? (i.e. mA mB)
Does ?
Is this what we expect?
Is it amazing?
no.
54
How are momentum and kinetic energy related? How
does the total momentum in an isolated system
change?
7-5 Elastic Collisions in One Dimension
Analyzing the solution for v'A and v'B
What happens if vB is equal to zero and mA is
equal to mB? (i.e. mA mB)
Does ?
Is this what we expect?
An example of this is Newtons Pendulum
Is it amazing?
no.
55
How are momentum and kinetic energy related? How
does the total momentum in an isolated system
change?
7-5 Elastic Collisions in One Dimension
Analyzing the solution for v'A and v'B
What happens if mB is equal to n times mA and
vA is equal to vB? (i.e. mB n mA and vA vB)
Does ?
Is this what we expect?
This is a special case known as Gutshalls
Pendulum
Is it amazing?
no.
56
How are momentum and kinetic energy related? How
does the total momentum in an isolated system
change?
Short-Range Elastic Collision Demonstration
What will the final velocity of each ball be
after the collision?
57
Pasco Momentum in Collisions LAB
How are momentum and kinetic energy related? How
does the total momentum in an isolated system
change?

• Work in groups of no more than 4 people.
• Return all supplies to the counter/cart.

INSERT LAB PICTURE
58
WebAssign/Lab Time
How are momentum and kinetic energy related? How
does the total momentum in an isolated system
change?

• Work on WebAssign Problems 7.1 - 7.14, or the
  Pasco Momentum in Collisions Lab
• Final Copy Criteria
• State the problem (Ex. Find displacement)
• Draw a picture/diagram
• Provide a list or table of all given data (Ex. ?t
  2 s)
• Solve the problem symbolically (Ex. v?x/?t ? ?x
  v?t)
• Plug in numbers and units to obtain answer. (Ex.
  ?x (5 m/s)(2 s) 10 m)
• Notes about WebAssign
• Positive vs. negative answers (Try a negative
  sign)
• Look at the final unit (hours or minutes or
  seconds)

59
How are momentum and kinetic energy related? How
does the total momentum in an isolated system
change?
Summary

• Answer the Essential Questions.
• Ticket out the Door
• What are two interesting things that you learned
  about elastic collisions during this class?
• (Note that any positive comments about the
  coolest general derivation shown to date, aka.
  Gutshalls Pendulum derivation, is EXTRA CREDIT)
• HW
• Pasco Momentum in Collisions Lab (Questions and
  Conclusions)
• WebAssign Problems 7.1 - 7.14

INSERTPICTURE
60
Day 4
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Inelastic Collisions

61
After Attendance
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Place HW on my desk
• Pickup and sign out your computer
• Log into www.plutonium-239.com
• Select the Warm-Up link
• Complete todays warm-up and submit it
• Logout and return the computer to the cart

62
Feed Back for Google Docs
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Was anything confusing on google docs?
• Noteworthy Student Responses

63
Review of Materials
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Yesterdays TOTD WebAssign Questions

64
Linear Momentum Inelastic Collisions

• EQ(s) How are momentum and kinetic energy
  related?

INSERT Lamborghini Crash Video
Start How are the final velocities of
Jerry-the-Race-Car-Driver and the infamous
telephone pole related after they collide?
65
How are momentum and kinetic energy related?
7-6 Inelastic Collisions
With inelastic collisions, some of the initial
kinetic energy is lost to thermal or potential
energy. It may also be gained during explosions,
as there is the addition of chemical or nuclear
energy. A completely inelastic collision is one
where the objects stick together afterwards, so
there is only one final velocity.
66
How are momentum and kinetic energy related?
7-6 Coefficient of Restitution, e
Recall that holds true for elastic
collisions, but for completely inelastic
collisions. Therefore it is useful to write
as
Where e is known as the coefficient of
restitution.
For elastic collisions, e 1 For completely
inelastic collisions, e 0 And for inelastic
collisions, 0 lt e lt 1.
67
How are momentum and kinetic energy related?
7-6 Coefficient of Restitution, e
A simple method for measuring the coefficient of
restitution for an object colliding with a very
hard surface is to drop the object onto a heavy
steel plate (vB v'B 0). We can then use
conservation of energy to derive a formula for e
in terms of the original height h and the maximum
height h' reached after one collision.
0
1
Note that v'A and vA are already in opposite
directions, therefore
68
How are momentum and kinetic energy related?
7-6 Coefficient of Restitution, e
A simple method for measuring the coefficient of
restitution for an object colliding with a very
hard surface is to drop the object onto a heavy
steel plate (vB v'B 0). We can then use
conservation of energy to derive a formula for e
in terms of the original height h and the maximum
height h' reached after one collision.
3
2
Note that v'A and vA are already in opposite
directions, therefore
69
Impulse and Inelastic Collisions
How are momentum and kinetic energy related?
Could we calculate final velocity with their data?
INSERT VIDEO CLIP
70
Impulse and Inelastic Collisions
How are momentum and kinetic energy related?
Could we calculate final velocity with their data?
INSERT VIDEO CLIP
71
Impulse and Inelastic Collisions
How are momentum and kinetic energy related?
Could we calculate final velocity with their data?
INSERT VIDEO CLIP
72
How are momentum and kinetic energy related?
Completely Inelastic Collision Demonstration
What will the final velocity of the dual-ball
combination be after the collision?
73
Impulse and Change in Momentum LAB
How are momentum and kinetic energy related?

• Work in groups of no more than 4 people.
• Return all supplies to the counter/cart.

74
WebAssign/Lab Time
How are momentum and kinetic energy related?

• Work on WebAssign Problems 7.1 - 7.18, the Pasco
  Momentum in Collisions Lab, or the Pasco Impulse
  and Change in Momentum Lab
• Final Copy Criteria
• State the problem (Ex. Find displacement)
• Draw a picture/diagram
• Provide a list or table of all given data (Ex. ?t
  2 s)
• Solve the problem symbolically (Ex. v?x/?t ? ?x
  v?t)
• Plug in numbers and units to obtain answer. (Ex.
  ?x (5 m/s)(2 s) 10 m)
• Notes about WebAssign
• Positive vs. negative answers (Try a negative
  sign)
• Look at the final unit (hours or minutes or
  seconds)

75
How are momentum and kinetic energy related?
Summary

• Answer the Essential Questions.
• Ticket out the Door
• What is v'A in reference to v'B in a completely
  inelastic collision?
• What are the equations for e(v) and e(h)?
• What is the value of e for a completely
  inelastic collision?
• HW
• Pasco Momentum in Collisions Lab (Questions and
  Conclusions)
• Pasco Impulse and Change in Momentum Lab
  (Questions and Conclusions)
• WebAssign Problems 7.1 - 7.18

76
Day 5
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Collisions in Two Dimensions

77
After Attendance
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Place HW on my desk
• Pickup and sign out your computer
• Log into www.plutonium-239.com
• Select the Warm-Up link
• Complete todays warm-up and submit it
• Logout and return the computer to the cart

78
Feed Back for Google Docs
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Was anything confusing on google docs?
• Noteworthy Student Responses

79
Review of Materials
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Yesterdays TOTD WebAssign Questions

80
Linear Momentum 2-D Elastic Collisions

• EQ(s) How are momentum and kinetic energy
  related?

Start Describe the motion of two balls after
impact if one stationary ball is hit off-center
by another ball?
mB
81
How are momentum and kinetic energy related?
7-7 Collisions in Two or Three Dimensions
Conservation of energy and momentum can also be
used to analyze collisions in two or three
dimensions, but unless the situation is very
simple, the math quickly becomes unwieldy.
Here, a moving object collides with an object
initially at rest. Knowing the masses and initial
velocities is not enough we need to know the
angles as well in order to find the final
velocities.
82
How are momentum and kinetic energy related?
7-7 Collisions in Two or Three Dimensions

• Problem solving
• Choose the system. If it is complex, subsystems
  may be chosen where one or more conservation laws
  apply.
• Is there an external force? If so, is the
  collision time short enough that you can ignore
  it?
• Draw diagrams of the initial and final
  situations, with momentum vectors labeled.
• Choose a coordinate system.

83
How are momentum and kinetic energy related?
7-7 Collisions in Two or Three Dimensions
5. Apply momentum conservation there will be one
equation for each dimension. 6. If the collision
is elastic, apply conservation of kinetic energy
as well. 7. Solve. 8. Check units and magnitudes
of result.
84
How are momentum and kinetic energy related?
Elastic Collisions in 2-D Equations
Conservation of Momentum in the x-direction
Conservation of Momentum in the y-direction
45º
If it is an elastic collision, Conservation of
Kinetic Energy may also be used
85
TITLE
How are momentum and kinetic energy related?
(Thought Question)?
INSERT VIDEO CLIP

• Youtube address

86
Impulse and Change in Momentum LAB
How are momentum and kinetic energy related?

• Work in groups of no more than 4 people.
• Return all supplies to the counter/cart.

87
WebAssign/Lab Time
How are momentum and kinetic energy related?

• Work on WebAssign Problems 7.1 - 7.19, the Pasco
  Momentum in Collisions Lab, or the Pasco Impulse
  and Change in Momentum Lab
• Final Copy Criteria
• State the problem (Ex. Find displacement)
• Draw a picture/diagram
• Provide a list or table of all given data (Ex. ?t
  2 s)
• Solve the problem symbolically (Ex. v?x/?t ? ?x
  v?t)
• Plug in numbers and units to obtain answer. (Ex.
  ?x (5 m/s)(2 s) 10 m)
• Notes about WebAssign
• Positive vs. negative answers (Try a negative
  sign)
• Look at the final unit (hours or minutes or
  seconds)

88
How are momentum and kinetic energy related?
Summary

• Answer the Essential Questions.
• Ticket out the Door
• During a 2-D collision, what is the ?p'y
• What trigonometric function is used to calculate
  the v'Ay?
• What trigonometric function is used to calculate
  the v'By?
• HW
• Pasco Momentum in Collisions Lab (Questions and
  Conclusions)
• Pasco Impulse and Change in Momentum Lab
  (Questions and Conclusions)
• WebAssign Problems 7.1 - 7.19

INSERTPICTURE
89
Day 6
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Center of Mass
• CM for the Human Body
• CM and Translational Motion

90
After Attendance
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Place HW on my desk
• Pickup and sign out your computer
• Log into www.plutonium-239.com
• Select the Warm-Up link
• Complete todays warm-up and submit it
• Logout and return the computer to the cart

91
Feed Back for Google Docs
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Was anything confusing on google docs?
• Noteworthy Student Responses

92
Review of Materials
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Yesterdays TOTD WebAssign Questions

93
Linear Momentum Center of Mass

• EQ(s) How are the center of mass (CM) and
  momentum related?

Start Why do high jumpers utilize the
flipperdipper flop technique to maximize their
jump height?
94
How are the center of mass (CM) and momentum
related?
7-8 Center of Mass
In (a), the divers motion is pure translation
in (b) it is translation plus rotation. There is
one point that moves in the same path a
particle would take if subjected to the same
force as the diver. This point is called the
center of mass (CM).
95
How are the center of mass (CM) and momentum
related?
7-8 Center of Mass
The general motion of an object can be considered
as the sum of the translational motion of the CM,
plus rotational, vibrational, or other forms of
motion about the CM.
96
How are the center of mass (CM) and momentum
related?
7-8 Center of Mass
For two particles, the center of mass lies closer
to the one with the most mass where M is the
total mass.
97
How are the center of mass (CM) and momentum
related?
7-8 Center of Mass
The center of gravity is the point where the
gravitational force can be considered to act. It
is the same as the center of mass as long as the
gravitational force does not vary among different
parts of the object.(i.e. Far away from a
blackhole)
98
How are the center of mass (CM) and momentum
related?
7-8 Center of Mass
The center of gravity can be found experimentally
by suspending an object from different points.
The CM need not be within the actual object a
doughnuts CM is in the center of the hole.
99
How are the center of mass (CM) and momentum
related?
7-9 CM for the Human Body
The xs in the small diagram mark the CM of the
listed body segments.
100
How are the center of mass (CM) and momentum
related?
7-9 CM for the Human Body
The location of the center of mass of the leg
(circled) will depend on the position of the leg.
101
How are the center of mass (CM) and momentum
related?
7-9 CM for the Human Body
High jumpers have developed a technique where
their CM actually passes under the bar as they go
over it. This allows them to clear higher bars.
102
Center of Gravity and the Limbo Bar
How are the center of mass (CM) and momentum
related?
Why do people contort their bodies to travel
under the bar?
INSERT VIDEO CLIP The LIMBO

• Youtube address

103
How are the center of mass (CM) and momentum
related?
7-10 Center of Mass and Translational Motion
IMPORTANT The total momentum of a system of
particles is equal to the product of the total
mass and the velocity of the center of mass. The
sum of all the forces acting on a system is equal
to the total mass of the system multiplied by the
acceleration of the center of mass
(7-11)
104
How are the center of mass (CM) and momentum
related?
7-10 Center of Mass and Translational Motion
This is particularly useful in the analysis of
separations and explosions the center of mass
(which may not correspond to the position of any
particle) continues to move according to the net
force.
105
Center of Mass and the Space Shuttle
How are the center of mass (CM) and momentum
related?
How does the separation of the rocket boosters
affect the motion of the space shuttle?
INSERT VIDEO CLIP Space Shuttle Rocket Boosters
Separatingfrom Space Shuttle

• Youtube address

106
Impulse and Change in Momentum LAB
How are the center of mass (CM) and momentum
related?

• Work in groups of no more than 4 people.
• Return all supplies to the counter/cart.

107
WebAssign/Lab Time
How are the center of mass (CM) and momentum
related?

• Work on WebAssign Problems 7.1 - 7.22, the Pasco
  Momentum in Collisions Lab, or the Pasco Impulse
  and Change in Momentum Lab
• Final Copy Criteria
• State the problem (Ex. Find displacement)
• Draw a picture/diagram
• Provide a list or table of all given data (Ex. ?t
  2 s)
• Solve the problem symbolically (Ex. v?x/?t ? ?x
  v?t)
• Plug in numbers and units to obtain answer. (Ex.
  ?x (5 m/s)(2 s) 10 m)
• Notes about WebAssign
• Positive vs. negative answers (Try a negative
  sign)
• Look at the final unit (hours or minutes or
  seconds)

108
How are the center of mass (CM) and momentum
related?
Summary

• Answer the Essential Questions.
• Ticket out the Door
• What is the equation that allows us to calculate
  the location of the center of mass?
• What happens to the motion of a projectile about
  its center of mass if the object breaks apart?
• Can pushing off of a freefalling elevators floor
  before impact actually decrease your maximum
  impact velocity?
• HW
• Pasco Momentum in Collisions Lab (Questions and
  Conclusions)
• Pasco Impulse and Change in Momentum Lab
  (Questions and Conclusions)
• WebAssign Problems 7.1 - 7.22

INSERTPICTURE
109
Day 7
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Work Day 1

110
After Attendance
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Place HW on my desk
• Pickup and sign out your computer
• Log into www.plutonium-239.com
• Select the Warm-Up link
• Complete todays warm-up and submit it
• Logout and return the computer to the cart

111
Feed Back for Google Docs
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Was anything confusing on google docs?
• Noteworthy Student Responses

112
Review of Materials
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Yesterdays TOTD WebAssign Questions

113
Linear Momentum

• UEQ(s) How does an objects mass distribution,
  interaction with other objects and force at a
  distance influence the objects motion?

INSERT Picture
Start GoogleDocs Warm-Up Activity
114
Impulse and Change in Momentum LAB
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Work in groups of no more than 4 people.
• Return all supplies to the counter/cart.

115
WebAssign/Lab Time
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Work on WebAssign Problems 7.1 - 7.22, the Pasco
  Momentum in Collisions Lab, or the Pasco Impulse
  and Change in Momentum Lab
• Final Copy Criteria
• State the problem (Ex. Find displacement)
• Draw a picture/diagram
• Provide a list or table of all given data (Ex. ?t
  2 s)
• Solve the problem symbolically (Ex. v?x/?t ? ?x
  v?t)
• Plug in numbers and units to obtain answer. (Ex.
  ?x (5 m/s)(2 s) 10 m)
• Notes about WebAssign
• Positive vs. negative answers (Try a negative
  sign)
• Look at the final unit (hours or minutes or
  seconds)

116
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?
Summary

• Answer the Essential Questions.
• 3-2-1
• 3 Things you know well for the test
• 2 Questions that you still have for the test
• 1 Thing you enjoyed from the Linear Momentum Unit
• HW
• Pasco Momentum in Collisions Lab (Questions and
  Conclusions)
• Pasco Impulse and Change in Momentum Lab
  (Questions and Conclusions)
• WebAssign Problems 7.1 - 7.22

INSERTPICTURE
117
Day 8
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Summary / Work Day 2

118
After Attendance(Concept Map)
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Place HW on my desk
• Pickup and sign out your computer
• Log into www.plutonium-239.com
• Select the Warm-Up link
• Complete todays warm-up and submit it
• Logout and return the computer to the cart
• Pull out your Conservation of Energy and
  Momentum Concept Map

119
Feed Back for Google Docs
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Was anything confusing on google docs?
• Noteworthy Student Responses

120
Review of Materials
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Yesterdays TOTD WebAssign Questions

121
Linear Momentum

• UEQ(s) How does an objects mass distribution,
  interaction with other objects and force at a
  distance influence the objects motion?

INSERT Picture
Start GoogleDocs Warm-Up Activity
122
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?
Summary of Chapter 7

• Momentum of an object
• Newtons second law
• Total momentum of an isolated system of objects
  is conserved.
• During a collision, the colliding objects can be
  considered to be an isolated system even if
  external forces exist, as long as they are not
  too large.
• Momentum will therefore be conserved during
  collisions.

123
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?
Summary of Chapter 7, cont.

• In an elastic collision, total kinetic energy is
  also conserved.
• In an inelastic collision, some kinetic energy
  is lost.
• In a completely inelastic collision, the two
  objects stick together after the collision.
• The center of mass of a system is the point at
  which external forces can be considered to act.

124
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?
Linear Momentum Essential Questions

• How can the velocity of an object be quantified
  in terms of its momentum?
• How are momentum, impulse, and force related?
• How are momentum and kinetic energy related?
• How are the center of mass (CM) and momentum
  related?
• How does the total momentum in an isolated
  system change?
• Answer these before the test.

125
Impulse and Change in Momentum LAB
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Work in groups of no more than 4 people.
• Return all supplies to the counter/cart.

126
EQ/WebAssign/Lab Time
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Answer the Essential Questions
• Work on WebAssign Problems 7.1 - 7.22, the Pasco
  Momentum in Collisions Lab, or the Pasco Impulse
  and Change in Momentum Lab
• Final Copy Criteria
• State the problem (Ex. Find displacement)
• Draw a picture/diagram
• Provide a list or table of all given data (Ex. ?t
  2 s)
• Solve the problem symbolically (Ex. v?x/?t ? ?x
  v?t)
• Plug in numbers and units to obtain answer. (Ex.
  ?x (5 m/s)(2 s) 10 m)
• Notes about WebAssign
• Positive vs. negative answers (Try a negative
  sign)
• Look at the final unit (hours or minutes or
  seconds)

127
Summary
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Ticket out the Door
• Write down two questions and their answer for the
  test tomorrow and turn it in.
• One conceptual problem
• One mathematical problem
• HW (Write down in your Student Planner)
• Answer the Essential Questions
• Pasco Momentum in Collisions Lab (Questions and
  Conclusions)
• Pasco Impulse and Change in Momentum Lab
  (Questions and Conclusions)
• WebAssign Problems 7.1 - 7.22
• WebAssign Final Copy

128
Day 10 Test
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Linear Momentum

129
After Attendance
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Place HW on my desk (in Reverse Alphabetical
  Order)
• WebAssign Final Copy
• Essential Questions
• Laboratory Assignment(s)
• Pickup the following
• Chapter 8 Vocabulary Acceleration
• Scantron Sheet
• Fill in the following on the scantron sheet
  front
• Name Write your name on it!!
• Subject PIM
• Test MOM
• Date S10
• Period Block 2

130
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?
Linear Momentum Test

• Do not write on Part I (the scantron questions)
• Put your name on Part II and complete it
• Verify any corrections below that have made
  before submitting your test.
• Complete the Chapter 8 Vocabulary Acceleration
• Test Corrections
• Question

131
Summary
UEQ How does an objects mass distribution,
interactions with other objects, and force at a
distance influence the objects motion?

• Submit your Linear Momentum Test
• HW
• Chapter 8 Vocabulary Acceleration